Question: Rewrite as a simplified fraction. ${1.\overline{1} = {?}}$
Solution: Let $x$ equal the decimal. Set up two equations such that the digits after the decimal point are identical. ${\begin{aligned}10x &= 11.1111...\\ 1x &= 1.1111...\end{aligned}}$ Subtracting the two equations, we have: ${9x = 10}$ ${x = \dfrac{10}{9}} \text{or} {1 \dfrac{1}{9}}$